The importance of students’ identity, power, and experiences

In this blog post, I point out that there is growing evidence that there some so-called “active learning” teaching strategies (on average) improve learning outcomes for all students while also (on average) improving learning outcomes disproportionately more for women, students of color, and/or first-generation students.
 
For example, in this paper, Sandra Laursen, Marja-Liisa Hassi, Marina Kogan, and Timonthy Weston investigate what undergraduate students report about their learning in Inquiry-Based Learning (IBL) mathematics courses:
…women in non-IBL courses reported statistically much lower gains than their male classmates in several important domains: understanding concepts, thinking and problem-solving, confidence, and positive attitude toward mathematics. In fact, both men and women reported higher learning gains from IBL courses than from non-IBL courses, but traditional teaching approaches did substantial disservice to women in particular, inhibiting their learning and reducing their confidence… Overall it appeared that non-IBL courses tended to reinforce prior achievement patterns, helping the “rich” to get “richer.” In contrast, IBL courses seemed to offer an extra boost to lower-achieving students, especially among pre-service teachers. Yet there was no evidence of harm done to the strongest students.
 
Now contrast that paper with this recent paper: Johnson, E., Andrews-Larson, C., Keene, K., Keller, R., Fortune, N., & Melhuish, K. (2018). Inquiry and inequity in the undergraduate mathematics classroom. Proceedings of the 40th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, pages 966-969.

These researchers looked at student learning in an Inquiry-Oriented Abstract Algebra (IOAA) course taught by 12 different instructors. They compared the performance of these students with those in more traditional Algebra courses at other institutions using the same content assessment instrument. They found that men and women performed similarly on the instrument in traditional courses but that men outperformed women slightly in their sample of IOAA courses. And, this performance gap was bigger for some of the 12 instructors than others.

How do we square the research of Laursen et al with that of Johnson et al?

1. First, the student sample size in the Laursen et al paper (over 3000) was much bigger than that for the Johnson et al paper (513). And, when the latter authors analyze student performance in specific instructors’ courses, those numbers are even smaller. It’s natural to have larger sampling variation with smaller samples.

And we’re talking about something much more complicated than taking samples from the same normal distribution. Two students might sit in the same course, listen to the same instructor, and do the same assignments, but might still have very different experiences in that class based on their life experiences, identities, interests, etc. Corresponding, their learning outcomes might be different too.

I see the Johnson et al paper as a warning to us all that it’s not enough just to employ some of these active learning instructional practices. We need to also be more intentionally inclusive as we teach in more active ways by paying attention to the experiences that students have in our courses. This reminder is also echoed by Elham Kazemi and Corey Drake in their plenary paper at the same PME-NA 40 conference (where Johnson and her colleagues presented their work). 

2. We should remember that these empirical papers measure student learning and/or attitudes under different conditions for learning but they don’t explain the mechanism behind why some students might benefit or be harmed by those conditions. In other words, it is still not clear why IBL courses seems to have a disproportionately positive effect on women in the paper by Laursen et al.

3. And, keep in mind that Laursen et al measured student self-reported gains while Johnson et al directly measured student learning on a content area assessment. We would expect self-reported learning gains to be strongly correlated with performance on a content assessment, but they aren’t the same thing.

Finally, how do we think about this work by Johnson et al in relation to this CBMS statement promoting active learning? How do we adopt a critical stance when studying these instructional practices without jeopardizing the movement toward broader adoption of active learning in our field?
 
Rochelle Gutiérrez’s dimensions of equity comes to mind (even though she is no longer using the term “equity”).
 
Gutiérrez, R., 2009. Framing equity: Helping students “play the game” and “change the game.”. Teaching for excellence and equity in mathematics, 1(1), pp.4-8.
(Gutiérrez’s diagram from pg 6 of TEEMv1n1)
When we tout active learning via studies that show that it can produce disproportionately positive effects for women, students of color, and other marginalized groups of students (and I have done this!), that primarily emphasizes the dominant axis of access/achievement, since those studies generally quantify equity via summative measures of learning. What is missing is a focus on the critical axis of identity and power, which can greatly affect how students actually experience the learning in our classes.

Defensiveness is a barrier to equity work

Defensiveness can be a barrier to effective communication, particularly when it involves receiving feedback from others or encountering information that contradicts what we believe about ourselves. For that reason, defensiveness can be a major barrier to becoming a more equitable educator. In this blog post, I’d like to dive deeper into this subject to think more deeply about what I can do to become a more equitable educator and how we can help our field move towards greater equity and justice.

A few months ago, I was teaching multi-variable calculus and drew the following vector field on the board.

vectorfield

When this happened during class, a student mentioned “Oh! It looks like a swastika” and I said that it was unintentional but didn’t change the diagram and just kept going on.

After class, one of my students came to tell me that another student felt uncomfortable with the swastika and with the way that I handled the situation. In that moment, I felt a rush of defensiveness. My initial instinct was to defend myself (to point out that the swastika has actually been used for centuries before the Nazis and the version that appeared in class is actually a different orientation from the Nazi swastika and is closer to the sacred symbol used in many Asian cultures (…and even now as I write this I still feel defensive and feel like I have to explain myself)). I didn’t say any of that. Thankfully, I just paused and apologized, expressed that it wasn’t my intention to be dismissive and didn’t realize that it had that impact, and said that I would be more careful with this example in the future. Later, I removed one of the red arrows above in the online version of the lecture notes.

I share this anecdote not to make any kind of judgment on the student who felt uncomfortable. I don’t want to get into a debate about political correctness or students who are fragile “snowflakes”. All that matters here is that a student felt uncomfortable, I received feedback about it, and that feedback helped me recognize how I will do better in the future. (In the future, I won’t shy away from this example, but I will take 30 seconds to share a bit of history about the symbol.)

What was the source of the defensiveness in that situation? I realize now that the first emotions I felt in that moment had to do with surprise and anger from being misunderstood: “How could anyone think that I would be so insensitive or oblivious as to use such a hateful symbol in my class? Don’t you know all the stuff I’ve done to promote equity and justice?” I really dislike the feelings that come with someone being offended or upset by something I said or did, when that was not my intention–lots of people feel this way. And, that, dear friends, is a common source of tension for many people about talking and thinking about equity. The recognition that our past deeds might have marginalized, discouraged, or discriminated against people of color, women, people with disabilities, LGBTQ people (list goes on…) runs smack into the thought “BUT I DIDN’T MEAN IT”. And yet, while the intent was not there, the impact can still be real.

How does defensiveness lead to undesirable outcomes? When receiving feedback from someone else, defensiveness shifts the focus from the issue at hand to our own emotions. In this situation, if I would have responded defensively, it would have shifted the attention away from the student who was uncomfortable to my own hurt feelings. And the reality here is that I had nothing here to lose except my own stupid ego by listening to and receiving the feedback.

I’m not saying that we instructors should not defend ourselves against baseless accusations. If it is really the case that there is no possible iota of truth in the feedback that I am given, then I can choose to reject the feedback, or perhaps actually defend myself. However, in this situation, there really was something that I could have done differently so the feedback was helpful. And, the power difference in the student-teacher relationship is important here. Because it takes so much more courage to say something to someone who has power over you, I believe that when instructors receive feedback like this we should listen carefully and err on the side of being generous.

Here’s another example of how defensiveness can be an impediment to thinking about and working toward greater equity. An imagined conversation snippet:

Person A: “I think when our department enacts policy X, that is a form of institutional racism.”
Person B: “What are you saying? I’m not racist!”

The words “racist” and “racism” can conjure up strong feelings and sometimes bring conversations about equity to a halt. The historical significance of the word “racist” (that it came into popular use in the 1930s in response to the Nazis) helps to explain why some people react so strongly to that word.

This kind of defensive reaction often stems from the contradiction between unjust outcomes or discriminatory behavior and a belief in oneself as a good and decent person: “How could students possibly suggest that I could be racist/sexist/*-ist? Don’t they know that I have been fighting for [XYZ cause] for longer than they have been alive?” As with the previous swastika anecdote, the defensiveness here has the effect of shifting the conversation away from the topic of discussion (a policy) to a person’s feelings.

To get move past my own defensiveness, I want to work toward having a thick skin but tender heart. I want to become less sensitive to the effects of any feedback and criticism on my ego, or my conceptions of who I am or want to be, and instead be more sensitive to the experiences of others. I would rather err on the side of being misunderstood than to misunderstand others. My problem is how to disrupt the surge of defensive emotions so that I can exercise enough cognitive control to react gracefully in that situation.

And as an educator who tries to help others move toward greater equity too, I think this deeper understanding of my own defensiveness will help in situations when I encounter defensiveness with others. Defensiveness often begets more defensiveness, so having a thick skin and tender heart can help to disrupt that cycle.

(Many thanks to Dylan Kane for encouraging me to think about this topic, and to Robin Wilson and Dagan Karp for their helpful feedback.)

The Ever-Present Challenges of Group Work

I have written previously about how group work is both great for students and difficult to do well. Today I had a conversation with a student and faculty member that reinforced these ideas again.

Prof. X, a faculty member that that I know, is trying to incorporate more small group work in an upper division mathematics class. Through a set of circumstances that are too complicated to explain here, today I happened to talk to Student S who is in Prof. X’s class. Student S shared some difficult moments that she experienced in the class recently.

(1) In one situation, Student S said that she was in a group of four students. The students were asked to answer questions on the back of a worksheet, which involved parsing some definitions on the front of the worksheet. Three of the students chose to forge ahead on the questions without reading the definitions first, referring to them when they needed them. She wanted to read the definitions first and understand them before moving on. They left her behind and she basically worked on the assignment by herself.

(2) In another situation, Student S was in a group of four and was the only female student. Each person in the group was given a different task to complete and had to explain how to do that task to the rest of the group.  When it was Student S’s turn to explain her task, a student in her group was a bit confused and another student jumped in and explained Student S’s task instead of letting her explain it. And, that student didn’t explain it correctly! But, Student S diplomatically corrected the situation by giving the correct explanation to her group and also helped the student who jumped in realize that it wasn’t right that she wasn’t given the chance to talk about her assigned task. Nevertheless, Student S said that this “mansplaining” happened two more times that day.

Experiences like these caused Student S to feel frustrated in these group work experiences. Student S also shared that she has had a difficult semester full of experiences that have caused her to doubt her mathematical abilities. I don’t know all of the details, but I do know that one of the reasons why active learning (and group work in particular) is so risky is that it puts students at risk of being judged by each other and the instructor as being incapable, slow, unprepared, less than.

I also happened today to talk to Prof. X, who genuinely wants to make his class a more welcoming and inclusive space by using group work. He shared with students some research showing that that group work helps improve student learning overall but also tends to have disproportionately large benefits for women, first-generation students, and students of color. That transparency is very important and most of us could probably benefit from being more transparent about the rationale for our instructional choices. However, there is a slight danger here that I hadn’t considered before: these research studies show positive results of using group work on average, but that research does not guarantee that individual students will always benefit from the effects of group work. In fact, my hunch is that the variance of experiences in active learning settings may be higher than in a more controlled lecture classroom format. So, while transparency is important, I also wonder about whether in sharing evidence for these instructional approaches we also need to be careful to avoid making students that don’t have good experiences as a result of those approaches feel bad about that.

Let no one misinterpret what I’m saying here as a pronouncement against active learning or group work–on the contrary, we should double-down on group work and active learning, recognizing that it is simultaneously beneficial for students and difficult to implement well. We instructors need to think carefully about how we deploy group work and other forms of active learning so as to mitigate any potential negative effects, as much as is possible. Here are three questions to ask ourselves to do so:

  1. Who is likely to benefit (as a result of me using group work or some other form of active learning)? Who is not?
  2. Who is likely to feel included? Who is not?
  3. How would I know if I need to intervene in some way?

To answer questions #1 and #2, I suggest we think of groups of students such as first-generation students, introverted students, students of color, students for whom English is not their first language, students with learning disabilities, students who have had bad experiences in a mathematics classroom, etc. For example, in the case of (1) above, it might be the case that the group work was inadvertently structured in a way that students who needed or wanted more time processing definitions were at a disadvantage. It would then be a good exercise to think about ways to mitigate the difference in experiences caused by the way the activity was structured.

Note about questions #1 and #2: Almost certainly students who come to class prepared are more likely to feel included or to benefit from your class activities compared to students who don’t come to class prepared–that is a difference that is expected and that you may or may not want to mitigate.  It’s those other unintended and unwanted consequences that we need to look for.

Regarding Question #3: Student S is a remarkable person who has enough self-assurance that she was able to have a long conversation with Prof. X about these difficult topics, which led Prof. X to make some changes to the class. But, that leads me to wonder: in the absence of having such thoughtful, well-composed, mature students as Student S, how would we find out about these kinds of problems in our class? We can’t be everywhere all at once in the room when group work is happening. If we don’t have mechanisms to gather student feedback, problems can go unnoticed and result in real harm to students.

These conversations today also remind me the important of setting and maintaining norms of behavior in the classroom. It’s easy to set up good norms. It’s much more difficult to maintain them and creating a culture in your classroom where those norms are pervasive.

The reason these conversations were so poignant for me is that I know Prof. X has the best intentions and is making a strong effort to be inclusive and welcoming and yet Student S experienced these discouraging situations. It made me wonder how ignorant I am about such things happening in my class.

 

Why should faculty care about diversity, equity and inclusion?

Sumi Pendakur and I recently published an article in the Notices of the American Mathematical Society entitled, “Advocating for Diversity and Inclusion in Faculty Hiring,” in which we offer some best practices for faculty searches. Though it was written for people in the mathematical sciences, the strategies and tactics we offer can be used by any faculty search committee.

We wanted to share with you a section of the paper that didn’t make it into the final printed version, due to space constraints. We both consider this section to be an important piece of the puzzle.

I’m going to label this missing text as “Section 0” because it comes before Section 1. (This text will probably make more sense if you read it in the context of the rest of the article.)

Section 0. Why should faculty care about diversity, equity and inclusion?

Ultimately, the degree to which our institutions are successful at increasing diversity, equity and inclusion depends on how our institutions and those connected to it see these things as vital to their mission (Smith, 2009; Taylor, Milem, Coleman, 2016). The more that we can articulate our own reasons for promoting diversity, the better we can share those with others and see how they are connected with the missions of our institutions.

One of the most important steps that departments can take to support diversity in faculty hiring is actually something that takes place long before the position is approved. That step is to come to a shared understanding as a department about what is meant by words like “diversity” and “inclusion” and how those things relate to the mission of the department. If your institution has a strong vision for diversity, that is always a good place to start. Coming up with a department diversity statement can be helpful, but written documents like these are helpful only as much as they are supported and enacted by individuals in the department.

There are many specific reasons why your department or institution might value diversity in the mathematical sciences. The following economic argument is cited by publications such as “Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future”: minority groups are increasing as a percentage of the U.S. population and if these groups are not well-represented in the STEM workforce, we will suffer from a shortage of innovators who will spur economic growth.

Another argument has to do with the quality of work that we produce as a discipline. Without a broad representation of people, we cannot be sure that our work in the mathematical sciences addresses all of the important issues that need to be addressed, or that we are addressing these issues having heard all of the voices that need to be heard. More equitable participation will increase the robustness of our discipline.
Leadership is a common educational goal at many institutions, and that can often be a way to connect the mission of the institution with diversity. In today’s global society, multicultural competence and awareness of the societal impacts of one’s work is an increasingly important component of being a leader.

The student success imperative is also tied to the vision of diversity held by the institution and the search committee. Recruitment, retention, and successful graduation of an increasingly diverse (racially, sexually, and socioeconomically) student body is directly impacted by multiple factors, including quality of faculty interaction and whether students see themselves reflected in the curriculum and in the faculty body. The powerful mentoring relationships of faculty of color and students of color are well-documented in the literature and contribute to the feeling of a welcoming and inclusive learning environment. In addition, critical mass of minoritized communities in both the student and faculty bodies reduces stereotype threat, thereby enhancing academic success.

Then, there are a whole range of arguments for diversity having to do with social justice. If your institution or department has a goal of graduating ethical people who contribute to society, one can make the argument that it is important for our students to understand their mathematical work in a historical context of exclusion and underrepresentation in the mathematical sciences in the U.S. Hiring faculty who have an understanding of the historical and sociological context of patterns of exclusion in our discipline and are able to integrate that knowledge into their teaching benefits ALL students.

If your department can find consensus around a set of arguments for diversity, equity and inclusion, it will be much more likely that its actions, including teaching practices, curricula, and faculty hiring practices, will support these outcomes. It will also make it less likely that a search committee will fall into the trap of making a false dichotomy between excellence and diversity; instead search committees will see that diversity is part of what it means to reach excellence by fulfilling its goals.

References mentioned in this excerpt:

Smith, Daryl. Diversity’s Promise for Higher Education: Making it Work. John Hopkins University Press, 2009.

Taylor, Teresa E., Jeffrey F. Milem, and Arthur F. Coleman (2016). Bridging the research to practice gap: Achieving mission-driven diversity and inclusion goals. New York,
NY: College Board. Available at https://www.aacu.org/node/16225.

Active Learning 2.0: Making it Inclusive

I’ve written several posts (1, 2, 3) about why active learning is a good thing. There is even growing evidence that some forms of active learning seem to raise student learning outcomes and make those outcomes more equitable at the same time.

All of that is great, but I believe strongly that active learning is not a magic bullet and can be implemented well or poorly. It can sometimes alienate students. A few years ago, I asked students to work in groups on a set of problems in complex analysis. I didn’t give any instructions on how to work well with each other and the problems were rather routine ones. That created a situation in which a student felt left behind in her group and she got discouraged. I tried to talk to her after class but it didn’t help and she dropped the class shortly after.  She said that she dropped the class because it didn’t fit into her schedule, but I still suspect that the group work experience had something to do with it.

In this post, I would like to argue that just using active learning is not enough. Because active learning requires students to be more engaged in their own learning and often involves more human-to-human interactions, we must pay attention to how those experiences support or diminish students’ sense of competence and belonging. I believe that in most cases, what’s needed is a little more care and planning in the use of active learning. I’ll try to illustrate that through some examples.

Example #1: Think-Pair-Share

A common active learning strategy is “think-pair-share“. Unfortunately, I often find that instructors skip the “think” step and skip to “pair and share.” And more generally, I find that most speakers/facilitators/instructors don’t give any (or sufficient) independent think time before asking participants/students to talk with one another.

In many situations, independent think time is so important because it gives time for people who process information in different ways to put together their thoughts before talking. Some people are great at “talking while thinking”: putting together their ideas while talking it out. It can work out well if you’re like this and you’re around other people who are similar–the process of building off of each others’ ideas mid-sentence is fun to watch. Unfortunately, I’m not one of those people. I prefer to have some time to think before I just start talking and I don’t like it when other people interrupt me when I’m talking.

By giving students independent think time before asking them to discuss, instructors can give students more equitable access to the opportunity to think. Students with learning differences, students whose first language is not English, students who are introverted will appreciate having more time to think before speaking. Even those students who like to “talk while thinking” will probably have more refined ideas to share before they start talking. Therefore, the independent think time makes discussions far more productive and less awkward.  I dislike those moments when I’m in a room of people and the speaker/instructor asks us to talk to each other and there’s this awkward period when people are trying to figure out what to say and who should start, etc.

Example #2: Open-Ended Projects

Do you assign open-ended projects in your classes? For example, in our introductory differential equations course, we often ask students create a model involving differential equations for some phenomena in their lives, then give a short presentation on it. It’s an assignment that spans several weeks and involves teams of three students working together.

These kinds of open-ended projects have all sorts of wonderful benefits: increased agency allows students to take more ownership over their learning; the open-ended nature of the task allow them to connect the course content with their own lived experiences; the chance to be creative makes the learning more memorable, fun, and motivating.

However, it is important to look at how these open-ended projects are structured for students. In particular, I am thinking of the work by Mary-Ann Winkelmes and others on the Transparency in Teaching and Learning (TILT) Project. If our instructions for these kinds of assignments don’t clearly convey to students why they should be personally invested, how to carry out the work, and how the work will be evaluated, we run the risk of making students bewildered and discouraged. That’s where it becomes helpful to be transparent about the purpose, tasks, and criteria for these open-ended projects. Of course, the tricky part is to balance being clear about processes and criteria while still maintaining high cognitive demand and room for creativity.

The reason this issue connects with equity is that not all students have had the benefit of having similar kinds of experiences in their previous education. Those that have often run with these kinds of open-ended tasks. Those that haven’t are likely to find the task so open-ended to be unsettling.

Here’s a nice way to see if your open-ended projects are written up in a way that students might find confusing: show your project instructions to a colleague in a different content area. Ask them what questions they might have as they read the instructions for your open-ended project. That will help to reveal some of the hidden assumptions that you might be making about what students know about these kinds of tasks. Being more transparent helps to put students on a more level playing field.

Example #3: Group Work

I saved this topic for last because I think it’s tricky to do well. The rewards and risks that accompany it are great.

If you assign students to work in heterogeneous ability groups (i.e., creating groups in which struggling students work with “more capable” students), there is always the risk of the groupings themselves to discourage students. Students aren’t dumb–they know that we sometimes group them in this way. If you are struggling in the class and you see that you’re always the one in the group that is struggling, and you’re not really getting the support you need from your peers, you might begin to wonder whether you really belong in the group and the class.  Students also don’t know how to help each other, especially in math classes–their understanding of what it means to help someone else usually involves telling someone a procedure or answer without providing any of the rationale.

But even if you group students in other ways, because you can’t be in all places at all times in the classroom, there is always the risk that one of your groups has negative interactions that spoil the learning for the group, or worse, cause some students to feel marginalized or excluded.

The example that I mentioned at the top of the post suggests a second reason why group work can go badly. When you ask students to work together on a task that really doesn’t require multiple brains, then you’re setting students up for to compare themselves with each other to see who can do it faster/better, or to zone out and copy the work of the “smart” student. If you’re going to have groups of students work together, then the task should really take advantage of the fact that multiple brains working together can accomplish more than those brains working in parallel but separately. In other words, you should use group worthy tasks.

Third, group work can go awry because we all have biases. The small groups in the classroom become microcosms of inequities that exist in the broader society. For example, if you have a group of three men and one woman working together, you might find that the three men ignore the contributions of the woman. Students need to learn how to work well with each other. Scan the classroom frequently for status issues (for example, by looking at each student’s body language and how much they are talking/contributing).

Finally, there is the challenge of establish and maintaining norms and expectations for group work (you have them, right?). If students aren’t familiar with your norms and expectations, you might want to find ways for students to practice working in groups before doing it in class on course content.

What other strategies do you use to ensure that active learning in your classroom supports the learning for all students? Please add your comments below.

Building Evidence Connecting Teaching Practices and More Equitable Student Outcomes (Continuously Updated)

Note: This post will be continuously updated as I gather more research on this topic.

In their paper “Active learning increases student performance in science, engineering, and mathematics,” Freeman, et al., suggest that we are seeing a new wave of “second-generation research” in the education literature that explores “which aspects of instructor behavior are most important for achieving the greatest gains with active learning, and elaborate on recent work indicating that underprepared and underrepresented students may benefit most from active methods.”

Indeed, a growing body of research shows that there are specific teaching strategies that (on average) improve learning outcomes for all students and also (on average) improve learning outcomes disproportionately for women and/or underrepresented students.

In this continuously updated blog post, I will try to maintain an annotated bibliography of such research. My goal is to provide higher education faculty and faculty developers with evidence to support teaching strategies that produce more equitable learning outcomes for all students, but particularly those who have been historically left out of STEM fields.


Huber, Bettina J., 2010. “Does Participation in Multiple High Impact Practices Affect Student Success at Cal State Northridge? Some Preliminary Insights” Northridge, CA: California State University-Northridge Office of Institutional Research.

National Survey of Student Engagement (NSSE) results from 863 graduating seniors at CSUN showed a correlation between HIP participation and higher GPA at exit and increased likelihood of graduating on time. Low-income students (Pell Grant recipients) and Latinx students had even higher GPA bump. Exit GPAs of Latinx and Pell students who didn’t participate in HIPs were lower than those of other students but if they participated in three or more HIPs their GPAs slightly exceeded other students.


Haak, D.C., HilleRisLambers, J., Pitre, E. and Freeman, S., 2011. Increased structure and active learning reduce the achievement gap in introductory biologyScience, 332(6034), pp.1213-1216.

“Highly structured” (daily and weekly practice with problem-solving, data analysis, higher-order cognitive skills) large-enrollment intro biology course for undergraduate majors at University of Washington improved learning for all students compared to low-structure (lecture intensive) version. There were disproportionately large benefits for students in their Educational Opportunity Program (many of whom are first-gen and from minority groups historically underrepresented in STEM).


Eddy, S.L. and Hogan, K.A., 2014. Getting under the hood: how and for whom does increasing course structure work?CBE-Life Sciences Education, 13(3), pp.453-468.

Essentially a replication of the 2011 study above except that the researchers studied differences between a “low structure” (lecture intensive), “moderate structure” (weekly ungraded preparatory assignments, 15-40% of each class for in-class activities on questions that were similar to previous exam problems) and “high structure” (even more prep assignments and in-class activities) for at the University of North Carolina. The same instructor taught all of the different versions of this course. Total of about 2400 students over 4 years of the study. Failure rate went down for all students in the more structured courses compared to lecture intensive version. Students also reported a greater sense of classroom community. Black students participated in the lecture intensive class far less than other students did, but in the more structured course, they spoke in class as much as other students. Exam grades improved for everyone in the moderate structure course, but it increased even more for Black students. In fact, Black students in the structured course outperformed the majority students in the lecture version of the course.And, a similar thing was observed for first-generation students.


Laursen, S.L., Hassi, M.L., Kogan, M. and Weston, T.J., 2014. Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution studyJournal for Research in Mathematics Education, 45(4), pp.406-418.

Over 3000 students across 100 different course sections in four colleges and universities were included in this study of “inquiry-based learning” (IBL) in mathematics classrooms. The students were all in a math or science major, excluding students who were preservice elementary or secondary teachers. Even though there was a range of different implementations of IBL, researchers found that students in IBL courses on average performed as well as or better than their non-IBL peers. IBL students also took as many or more math courses than non-IBL students, which seems to indicate that their interest in mathematics increased as well. Pre- and post-surveys of cognitive skills in mathematics, attitudes toward mathematics, and attitudes about collaboration in a math class. Women in non-IBL courses reported significant decreases in their confidence to pursue higher mathematics, whereas men in non-IBL courses reported an increase in their confidence. In contrast, women in IBL courses reported an increase in their confidence similar to that of men in non-IBL courses.


Winkelmes, M.A., Bernacki, M., Butler, J., Zochowski, M., Golanics, J. and Weavil, K.H., 2016. A Teaching Intervention that Increases Underserved College Students’ SuccessPeer Review18(1/2).

The researchers set out to measure the effect of teachers providing two transparently designed, problem-based take-home assignments (as compared to their original versions) on first-year college students. (“Transparently designed” here means something specific to the training that the faculty received. They were trained to revise their assignments to be clearer about the purpose, tasks, and criteria for the assignments.) About 1,180 students taught by 35 faculty, 61 courses, 7 institutions were involved in the study. Because the courses spanned many different disciplines, the researchers relied mostly on self-report data from the students. “Students who received more transparency reported gains in three areas that are important predictors of students’ success: academic confidence, sense of belonging, and mastery of the skills that employers value most when hiring.” And what’s more, for first-generation, low-income, and underrepresented students, those reported benefits were larger.


Please let me know if you encounter other research articles that provide evidence for specific teaching strategies having disproportionately positive outcomes for women and/or students historically underrepresented from STEM. I will add it to this list.

Growth Mindset and Learning about Equity, Diversity, and Inclusion

Why is it so hard for people to talk and learn about equity, diversity, and inclusion? In this post I argue that part of the answer is that many people have a fixed mindset when it comes to learning about these things.

Carol Dweck’s work on fixed and growth mindset helps to explain why people react differently to challenging situations. In broad strokes, people with a growth mindset believe that ability (as it relates to that situation) can be developed, even when one fails to overcome that challenging situation; people with a fixed mindset approach the same challenging situation with doubt about their ability to overcome the situation despite hard work and they withdraw from the situation to avoid failing.

Mindset changes over time. And, mindset can vary by domain of knowledge–in other words, my self-concept as a learner of mathematics is high and I have a growth mindset about learning mathematics but my self-concept as an athlete is low and I have a fixed mindset about learning sports. (Sidenote: it is important to remember that growth mindset is not a silver bullet–most school-based interventions involving growth mindset have been shown to yield modest effects–and that growth mindset doesn’t make up for inequities in educational opportunities in our society.)

All of us need to learn more about equity, diversity, and inclusion, especially those of us who are teachers. We need to learn about the difference between race and ethnicity, sex and gender identity. We need to learn about our own implicit biases. We need to learn about racism, sexism, ableism, and all other forms of discrimination and bias, at the personal, institutional, and societal levels.

Learning about equity, diversity, and inclusion can be scary, especially for progressive, liberal-minded folks who want to believe that we are fair and good. The thought of being labeled as a racist, sexist, *-ist person can be frightening. However, the truth is that we all carry unconscious biases that cause us to exhibit prejudice despite our best intentions. Instead of thinking of being racist as a binary state, I posit that it is more meaningful and accurate to think of ourselves as being on a journey toward ever more equitable, inclusive, and caring words and actions. We’ll never fully get there, but we still work toward that goal.

There are interesting parallels between ways that people think about learning mathematics and ways that people think about equity, diversity, and inclusion. These parallels have to do with the beliefs that people have about their abilities and the ways that they approach challenging situations. Being racist is not an innate character trait in the same way that having the ability to learn math is not a product of one’s genes.

Fixed Mindset Growth Mindset
Learning math “I’m not good at math. My sister has the math brain in the family.” (implying that there is some sort of “math gene” that they lack and that math skill is a binary trait) “I can learn math with effort and persistence.”
Learning about equity, diversity, and inclusion “I’m a good person. I’m not racist.” (denying the existence of implicit bias, and implying that being racist is a binary trait) “I can learn more about these things with effort and persistence.”
Learning math “I don’t want to attempt this mathematical task because I’m likely to fail and I don’t want to be seen as dumb.” “I will try to learn what is needed for me to attempt this and if I mess up I will learn from that experience.”
Learning about equity, diversity, and inclusion “I can’t raise any controversial topics in my class because I might say the wrong thing and I don’t want to be seen as racist.” “I will try to learn what is needed for me to attempt this and if I mess up I will learn from that experience.”

I draw these parallels because I suspect that appealing to growth mindset might help some educators be more willing to talk about equity, diversity, and inclusion. Many educators are already familiar with the idea of a growth mindset and actively think about how to use it in their own teaching, so they might be able to see how it also applies to learning about equity, diversity, and inclusion. Most educators I know are trying to do the right thing and aren’t overtly racist and sexist. And yet, we still need to work harder to help more folks see equity, diversity, and inclusion as central to their work.

But a growth mindset approach is not enough. For folks who train others on topics relating to equity, diversity, and inclusion, it is important to set a tone of compassion and humility. Shame and guilt often cause people to withdraw from the conversation and put up defenses.

It doesn’t help that we seem to live in an age when people’s mistakes can be captured on video and shared around the world instantly. Call-out culture makes people nervous about saying or doing the wrong thing. And, our human nature is to want to discredit a person or organization entirely once we’ve found some flaw in them/it. The pressure to be perfect is so great–I understand why some faculty want to just sit on the sidelines and avoid saying anything that could be used against them.

We desperately need to transform classrooms and schools into spaces in which instructors and students can be brave with each other and at the same time offer grace to each other when mistakes occur. Part of the solution is to establish classroom norms that foster these things. (See previous post about some possible norms to use.) Part of the solution might also be to use the growth/fixed mindset framework to help debunk myths about ourselves. I invite you to share other things that could also help in the comment section below.